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    1: *> \brief <b> DSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DSYEVX + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevx.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevx.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevx.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
   22: *                          ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK,
   23: *                          IFAIL, INFO )
   24: * 
   25: *       .. Scalar Arguments ..
   26: *       CHARACTER          JOBZ, RANGE, UPLO
   27: *       INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
   28: *       DOUBLE PRECISION   ABSTOL, VL, VU
   29: *       ..
   30: *       .. Array Arguments ..
   31: *       INTEGER            IFAIL( * ), IWORK( * )
   32: *       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
   33: *       ..
   34: *  
   35: *
   36: *> \par Purpose:
   37: *  =============
   38: *>
   39: *> \verbatim
   40: *>
   41: *> DSYEVX computes selected eigenvalues and, optionally, eigenvectors
   42: *> of a real symmetric matrix A.  Eigenvalues and eigenvectors can be
   43: *> selected by specifying either a range of values or a range of indices
   44: *> for the desired eigenvalues.
   45: *> \endverbatim
   46: *
   47: *  Arguments:
   48: *  ==========
   49: *
   50: *> \param[in] JOBZ
   51: *> \verbatim
   52: *>          JOBZ is CHARACTER*1
   53: *>          = 'N':  Compute eigenvalues only;
   54: *>          = 'V':  Compute eigenvalues and eigenvectors.
   55: *> \endverbatim
   56: *>
   57: *> \param[in] RANGE
   58: *> \verbatim
   59: *>          RANGE is CHARACTER*1
   60: *>          = 'A': all eigenvalues will be found.
   61: *>          = 'V': all eigenvalues in the half-open interval (VL,VU]
   62: *>                 will be found.
   63: *>          = 'I': the IL-th through IU-th eigenvalues will be found.
   64: *> \endverbatim
   65: *>
   66: *> \param[in] UPLO
   67: *> \verbatim
   68: *>          UPLO is CHARACTER*1
   69: *>          = 'U':  Upper triangle of A is stored;
   70: *>          = 'L':  Lower triangle of A is stored.
   71: *> \endverbatim
   72: *>
   73: *> \param[in] N
   74: *> \verbatim
   75: *>          N is INTEGER
   76: *>          The order of the matrix A.  N >= 0.
   77: *> \endverbatim
   78: *>
   79: *> \param[in,out] A
   80: *> \verbatim
   81: *>          A is DOUBLE PRECISION array, dimension (LDA, N)
   82: *>          On entry, the symmetric matrix A.  If UPLO = 'U', the
   83: *>          leading N-by-N upper triangular part of A contains the
   84: *>          upper triangular part of the matrix A.  If UPLO = 'L',
   85: *>          the leading N-by-N lower triangular part of A contains
   86: *>          the lower triangular part of the matrix A.
   87: *>          On exit, the lower triangle (if UPLO='L') or the upper
   88: *>          triangle (if UPLO='U') of A, including the diagonal, is
   89: *>          destroyed.
   90: *> \endverbatim
   91: *>
   92: *> \param[in] LDA
   93: *> \verbatim
   94: *>          LDA is INTEGER
   95: *>          The leading dimension of the array A.  LDA >= max(1,N).
   96: *> \endverbatim
   97: *>
   98: *> \param[in] VL
   99: *> \verbatim
  100: *>          VL is DOUBLE PRECISION
  101: *> \endverbatim
  102: *>
  103: *> \param[in] VU
  104: *> \verbatim
  105: *>          VU is DOUBLE PRECISION
  106: *>          If RANGE='V', the lower and upper bounds of the interval to
  107: *>          be searched for eigenvalues. VL < VU.
  108: *>          Not referenced if RANGE = 'A' or 'I'.
  109: *> \endverbatim
  110: *>
  111: *> \param[in] IL
  112: *> \verbatim
  113: *>          IL is INTEGER
  114: *> \endverbatim
  115: *>
  116: *> \param[in] IU
  117: *> \verbatim
  118: *>          IU is INTEGER
  119: *>          If RANGE='I', the indices (in ascending order) of the
  120: *>          smallest and largest eigenvalues to be returned.
  121: *>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
  122: *>          Not referenced if RANGE = 'A' or 'V'.
  123: *> \endverbatim
  124: *>
  125: *> \param[in] ABSTOL
  126: *> \verbatim
  127: *>          ABSTOL is DOUBLE PRECISION
  128: *>          The absolute error tolerance for the eigenvalues.
  129: *>          An approximate eigenvalue is accepted as converged
  130: *>          when it is determined to lie in an interval [a,b]
  131: *>          of width less than or equal to
  132: *>
  133: *>                  ABSTOL + EPS *   max( |a|,|b| ) ,
  134: *>
  135: *>          where EPS is the machine precision.  If ABSTOL is less than
  136: *>          or equal to zero, then  EPS*|T|  will be used in its place,
  137: *>          where |T| is the 1-norm of the tridiagonal matrix obtained
  138: *>          by reducing A to tridiagonal form.
  139: *>
  140: *>          Eigenvalues will be computed most accurately when ABSTOL is
  141: *>          set to twice the underflow threshold 2*DLAMCH('S'), not zero.
  142: *>          If this routine returns with INFO>0, indicating that some
  143: *>          eigenvectors did not converge, try setting ABSTOL to
  144: *>          2*DLAMCH('S').
  145: *>
  146: *>          See "Computing Small Singular Values of Bidiagonal Matrices
  147: *>          with Guaranteed High Relative Accuracy," by Demmel and
  148: *>          Kahan, LAPACK Working Note #3.
  149: *> \endverbatim
  150: *>
  151: *> \param[out] M
  152: *> \verbatim
  153: *>          M is INTEGER
  154: *>          The total number of eigenvalues found.  0 <= M <= N.
  155: *>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
  156: *> \endverbatim
  157: *>
  158: *> \param[out] W
  159: *> \verbatim
  160: *>          W is DOUBLE PRECISION array, dimension (N)
  161: *>          On normal exit, the first M elements contain the selected
  162: *>          eigenvalues in ascending order.
  163: *> \endverbatim
  164: *>
  165: *> \param[out] Z
  166: *> \verbatim
  167: *>          Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
  168: *>          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
  169: *>          contain the orthonormal eigenvectors of the matrix A
  170: *>          corresponding to the selected eigenvalues, with the i-th
  171: *>          column of Z holding the eigenvector associated with W(i).
  172: *>          If an eigenvector fails to converge, then that column of Z
  173: *>          contains the latest approximation to the eigenvector, and the
  174: *>          index of the eigenvector is returned in IFAIL.
  175: *>          If JOBZ = 'N', then Z is not referenced.
  176: *>          Note: the user must ensure that at least max(1,M) columns are
  177: *>          supplied in the array Z; if RANGE = 'V', the exact value of M
  178: *>          is not known in advance and an upper bound must be used.
  179: *> \endverbatim
  180: *>
  181: *> \param[in] LDZ
  182: *> \verbatim
  183: *>          LDZ is INTEGER
  184: *>          The leading dimension of the array Z.  LDZ >= 1, and if
  185: *>          JOBZ = 'V', LDZ >= max(1,N).
  186: *> \endverbatim
  187: *>
  188: *> \param[out] WORK
  189: *> \verbatim
  190: *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
  191: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  192: *> \endverbatim
  193: *>
  194: *> \param[in] LWORK
  195: *> \verbatim
  196: *>          LWORK is INTEGER
  197: *>          The length of the array WORK.  LWORK >= 1, when N <= 1;
  198: *>          otherwise 8*N.
  199: *>          For optimal efficiency, LWORK >= (NB+3)*N,
  200: *>          where NB is the max of the blocksize for DSYTRD and DORMTR
  201: *>          returned by ILAENV.
  202: *>
  203: *>          If LWORK = -1, then a workspace query is assumed; the routine
  204: *>          only calculates the optimal size of the WORK array, returns
  205: *>          this value as the first entry of the WORK array, and no error
  206: *>          message related to LWORK is issued by XERBLA.
  207: *> \endverbatim
  208: *>
  209: *> \param[out] IWORK
  210: *> \verbatim
  211: *>          IWORK is INTEGER array, dimension (5*N)
  212: *> \endverbatim
  213: *>
  214: *> \param[out] IFAIL
  215: *> \verbatim
  216: *>          IFAIL is INTEGER array, dimension (N)
  217: *>          If JOBZ = 'V', then if INFO = 0, the first M elements of
  218: *>          IFAIL are zero.  If INFO > 0, then IFAIL contains the
  219: *>          indices of the eigenvectors that failed to converge.
  220: *>          If JOBZ = 'N', then IFAIL is not referenced.
  221: *> \endverbatim
  222: *>
  223: *> \param[out] INFO
  224: *> \verbatim
  225: *>          INFO is INTEGER
  226: *>          = 0:  successful exit
  227: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  228: *>          > 0:  if INFO = i, then i eigenvectors failed to converge.
  229: *>                Their indices are stored in array IFAIL.
  230: *> \endverbatim
  231: *
  232: *  Authors:
  233: *  ========
  234: *
  235: *> \author Univ. of Tennessee 
  236: *> \author Univ. of California Berkeley 
  237: *> \author Univ. of Colorado Denver 
  238: *> \author NAG Ltd. 
  239: *
  240: *> \date November 2011
  241: *
  242: *> \ingroup doubleSYeigen
  243: *
  244: *  =====================================================================
  245:       SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
  246:      $                   ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK,
  247:      $                   IFAIL, INFO )
  248: *
  249: *  -- LAPACK driver routine (version 3.4.0) --
  250: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  251: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  252: *     November 2011
  253: *
  254: *     .. Scalar Arguments ..
  255:       CHARACTER          JOBZ, RANGE, UPLO
  256:       INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
  257:       DOUBLE PRECISION   ABSTOL, VL, VU
  258: *     ..
  259: *     .. Array Arguments ..
  260:       INTEGER            IFAIL( * ), IWORK( * )
  261:       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
  262: *     ..
  263: *
  264: * =====================================================================
  265: *
  266: *     .. Parameters ..
  267:       DOUBLE PRECISION   ZERO, ONE
  268:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
  269: *     ..
  270: *     .. Local Scalars ..
  271:       LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
  272:      $                   WANTZ
  273:       CHARACTER          ORDER
  274:       INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
  275:      $                   INDISP, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
  276:      $                   ITMP1, J, JJ, LLWORK, LLWRKN, LWKMIN,
  277:      $                   LWKOPT, NB, NSPLIT
  278:       DOUBLE PRECISION   ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
  279:      $                   SIGMA, SMLNUM, TMP1, VLL, VUU
  280: *     ..
  281: *     .. External Functions ..
  282:       LOGICAL            LSAME
  283:       INTEGER            ILAENV
  284:       DOUBLE PRECISION   DLAMCH, DLANSY
  285:       EXTERNAL           LSAME, ILAENV, DLAMCH, DLANSY
  286: *     ..
  287: *     .. External Subroutines ..
  288:       EXTERNAL           DCOPY, DLACPY, DORGTR, DORMTR, DSCAL, DSTEBZ,
  289:      $                   DSTEIN, DSTEQR, DSTERF, DSWAP, DSYTRD, XERBLA
  290: *     ..
  291: *     .. Intrinsic Functions ..
  292:       INTRINSIC          MAX, MIN, SQRT
  293: *     ..
  294: *     .. Executable Statements ..
  295: *
  296: *     Test the input parameters.
  297: *
  298:       LOWER = LSAME( UPLO, 'L' )
  299:       WANTZ = LSAME( JOBZ, 'V' )
  300:       ALLEIG = LSAME( RANGE, 'A' )
  301:       VALEIG = LSAME( RANGE, 'V' )
  302:       INDEIG = LSAME( RANGE, 'I' )
  303:       LQUERY = ( LWORK.EQ.-1 )
  304: *
  305:       INFO = 0
  306:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  307:          INFO = -1
  308:       ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
  309:          INFO = -2
  310:       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
  311:          INFO = -3
  312:       ELSE IF( N.LT.0 ) THEN
  313:          INFO = -4
  314:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  315:          INFO = -6
  316:       ELSE
  317:          IF( VALEIG ) THEN
  318:             IF( N.GT.0 .AND. VU.LE.VL )
  319:      $         INFO = -8
  320:          ELSE IF( INDEIG ) THEN
  321:             IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
  322:                INFO = -9
  323:             ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
  324:                INFO = -10
  325:             END IF
  326:          END IF
  327:       END IF
  328:       IF( INFO.EQ.0 ) THEN
  329:          IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  330:             INFO = -15
  331:          END IF
  332:       END IF
  333: *
  334:       IF( INFO.EQ.0 ) THEN
  335:          IF( N.LE.1 ) THEN
  336:             LWKMIN = 1
  337:             WORK( 1 ) = LWKMIN
  338:          ELSE
  339:             LWKMIN = 8*N
  340:             NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
  341:             NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) )
  342:             LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
  343:             WORK( 1 ) = LWKOPT
  344:          END IF
  345: *
  346:          IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
  347:      $      INFO = -17
  348:       END IF
  349: *
  350:       IF( INFO.NE.0 ) THEN
  351:          CALL XERBLA( 'DSYEVX', -INFO )
  352:          RETURN
  353:       ELSE IF( LQUERY ) THEN
  354:          RETURN
  355:       END IF
  356: *
  357: *     Quick return if possible
  358: *
  359:       M = 0
  360:       IF( N.EQ.0 ) THEN
  361:          RETURN
  362:       END IF
  363: *
  364:       IF( N.EQ.1 ) THEN
  365:          IF( ALLEIG .OR. INDEIG ) THEN
  366:             M = 1
  367:             W( 1 ) = A( 1, 1 )
  368:          ELSE
  369:             IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN
  370:                M = 1
  371:                W( 1 ) = A( 1, 1 )
  372:             END IF
  373:          END IF
  374:          IF( WANTZ )
  375:      $      Z( 1, 1 ) = ONE
  376:          RETURN
  377:       END IF
  378: *
  379: *     Get machine constants.
  380: *
  381:       SAFMIN = DLAMCH( 'Safe minimum' )
  382:       EPS = DLAMCH( 'Precision' )
  383:       SMLNUM = SAFMIN / EPS
  384:       BIGNUM = ONE / SMLNUM
  385:       RMIN = SQRT( SMLNUM )
  386:       RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
  387: *
  388: *     Scale matrix to allowable range, if necessary.
  389: *
  390:       ISCALE = 0
  391:       ABSTLL = ABSTOL
  392:       IF( VALEIG ) THEN
  393:          VLL = VL
  394:          VUU = VU
  395:       END IF
  396:       ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
  397:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
  398:          ISCALE = 1
  399:          SIGMA = RMIN / ANRM
  400:       ELSE IF( ANRM.GT.RMAX ) THEN
  401:          ISCALE = 1
  402:          SIGMA = RMAX / ANRM
  403:       END IF
  404:       IF( ISCALE.EQ.1 ) THEN
  405:          IF( LOWER ) THEN
  406:             DO 10 J = 1, N
  407:                CALL DSCAL( N-J+1, SIGMA, A( J, J ), 1 )
  408:    10       CONTINUE
  409:          ELSE
  410:             DO 20 J = 1, N
  411:                CALL DSCAL( J, SIGMA, A( 1, J ), 1 )
  412:    20       CONTINUE
  413:          END IF
  414:          IF( ABSTOL.GT.0 )
  415:      $      ABSTLL = ABSTOL*SIGMA
  416:          IF( VALEIG ) THEN
  417:             VLL = VL*SIGMA
  418:             VUU = VU*SIGMA
  419:          END IF
  420:       END IF
  421: *
  422: *     Call DSYTRD to reduce symmetric matrix to tridiagonal form.
  423: *
  424:       INDTAU = 1
  425:       INDE = INDTAU + N
  426:       INDD = INDE + N
  427:       INDWRK = INDD + N
  428:       LLWORK = LWORK - INDWRK + 1
  429:       CALL DSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ),
  430:      $             WORK( INDTAU ), WORK( INDWRK ), LLWORK, IINFO )
  431: *
  432: *     If all eigenvalues are desired and ABSTOL is less than or equal to
  433: *     zero, then call DSTERF or DORGTR and SSTEQR.  If this fails for
  434: *     some eigenvalue, then try DSTEBZ.
  435: *
  436:       TEST = .FALSE.
  437:       IF( INDEIG ) THEN
  438:          IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
  439:             TEST = .TRUE.
  440:          END IF
  441:       END IF
  442:       IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
  443:          CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
  444:          INDEE = INDWRK + 2*N
  445:          IF( .NOT.WANTZ ) THEN
  446:             CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
  447:             CALL DSTERF( N, W, WORK( INDEE ), INFO )
  448:          ELSE
  449:             CALL DLACPY( 'A', N, N, A, LDA, Z, LDZ )
  450:             CALL DORGTR( UPLO, N, Z, LDZ, WORK( INDTAU ),
  451:      $                   WORK( INDWRK ), LLWORK, IINFO )
  452:             CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
  453:             CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
  454:      $                   WORK( INDWRK ), INFO )
  455:             IF( INFO.EQ.0 ) THEN
  456:                DO 30 I = 1, N
  457:                   IFAIL( I ) = 0
  458:    30          CONTINUE
  459:             END IF
  460:          END IF
  461:          IF( INFO.EQ.0 ) THEN
  462:             M = N
  463:             GO TO 40
  464:          END IF
  465:          INFO = 0
  466:       END IF
  467: *
  468: *     Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
  469: *
  470:       IF( WANTZ ) THEN
  471:          ORDER = 'B'
  472:       ELSE
  473:          ORDER = 'E'
  474:       END IF
  475:       INDIBL = 1
  476:       INDISP = INDIBL + N
  477:       INDIWO = INDISP + N
  478:       CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
  479:      $             WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
  480:      $             IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
  481:      $             IWORK( INDIWO ), INFO )
  482: *
  483:       IF( WANTZ ) THEN
  484:          CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
  485:      $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
  486:      $                WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
  487: *
  488: *        Apply orthogonal matrix used in reduction to tridiagonal
  489: *        form to eigenvectors returned by DSTEIN.
  490: *
  491:          INDWKN = INDE
  492:          LLWRKN = LWORK - INDWKN + 1
  493:          CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
  494:      $                LDZ, WORK( INDWKN ), LLWRKN, IINFO )
  495:       END IF
  496: *
  497: *     If matrix was scaled, then rescale eigenvalues appropriately.
  498: *
  499:    40 CONTINUE
  500:       IF( ISCALE.EQ.1 ) THEN
  501:          IF( INFO.EQ.0 ) THEN
  502:             IMAX = M
  503:          ELSE
  504:             IMAX = INFO - 1
  505:          END IF
  506:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
  507:       END IF
  508: *
  509: *     If eigenvalues are not in order, then sort them, along with
  510: *     eigenvectors.
  511: *
  512:       IF( WANTZ ) THEN
  513:          DO 60 J = 1, M - 1
  514:             I = 0
  515:             TMP1 = W( J )
  516:             DO 50 JJ = J + 1, M
  517:                IF( W( JJ ).LT.TMP1 ) THEN
  518:                   I = JJ
  519:                   TMP1 = W( JJ )
  520:                END IF
  521:    50       CONTINUE
  522: *
  523:             IF( I.NE.0 ) THEN
  524:                ITMP1 = IWORK( INDIBL+I-1 )
  525:                W( I ) = W( J )
  526:                IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
  527:                W( J ) = TMP1
  528:                IWORK( INDIBL+J-1 ) = ITMP1
  529:                CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
  530:                IF( INFO.NE.0 ) THEN
  531:                   ITMP1 = IFAIL( I )
  532:                   IFAIL( I ) = IFAIL( J )
  533:                   IFAIL( J ) = ITMP1
  534:                END IF
  535:             END IF
  536:    60    CONTINUE
  537:       END IF
  538: *
  539: *     Set WORK(1) to optimal workspace size.
  540: *
  541:       WORK( 1 ) = LWKOPT
  542: *
  543:       RETURN
  544: *
  545: *     End of DSYEVX
  546: *
  547:       END